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## #1 2006-11-07 12:44:08

Neha
Member
Registered: 2006-10-11
Posts: 173

### systems

solve the system of equations by the substitution method:

a + 1/2b = 16
2a + b = 50

ok i know how to do equations such as these but this has a fraction......so help

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## #2 2006-11-07 15:37:52

pi man
Member
Registered: 2006-07-06
Posts: 251

### Re: systems

Multiply both sides of the 1st equation by 2:

Multiply both sides by b:

You can use the quadratic formula to solve this now.

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## #3 2006-11-08 04:38:51

Neha
Member
Registered: 2006-10-11
Posts: 173

### Re: systems

ok thanks
i haev do the quadratic formula....
and stoped here
x = 18 +- sqrt(-320) / 2

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## #4 2006-11-09 02:07:54

Neha
Member
Registered: 2006-10-11
Posts: 173

### Re: systems

hello guys what to do next......
18 +- sqrt(-320)
x = -------------------
2

help

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## #5 2006-11-11 08:09:36

Neha
Member
Registered: 2006-10-11
Posts: 173

### Re: systems

I THINK YOU WRONG

a+1/2b=16
2a+b=50
2a=50-b
a=(50-b)/2
substituting in eqn. 1
(50-b)/2+1/2b=16
multiplying by 2b
b(50-b)+1=32b
50b-b^2+1-32b=0
-b^2+18b+1=0
=>b^2-18b-1=0
b=[18+/-rt(324+4)]/2
=[9+/-rt82]
similarly express b interms of a and find a
or substitute the value of a
i have a feeling your sum might be
a+(1/2)*b=16
and 2a+b=50
these are the equations of parallel lines
and hence no solution

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## #6 2006-11-11 13:40:13

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: systems

b!=0

Last edited by krassi_holmz (2006-11-11 13:47:43)

IPBLE:  Increasing Performance By Lowering Expectations.

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## #7 2006-11-11 13:53:52

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: systems

a + 1/2b = 16
2a + b = 50

Twice it was assumed that it is 1/(2b) in the first equation, where as I'm pretty sure it is in fact (1/2)b.

Normally students are asked to solve systems of linear equations.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #8 2006-11-11 13:59:20

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: systems

If it's (1/2)b:

No solution.

IPBLE:  Increasing Performance By Lowering Expectations.

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